Research of the isogeny graph structure of supersingular curves for post-quantum cryptography protocols

Isogeny graphs of supersingular elliptic curves are one of perspective mathematical structures for post-quantum cryptography algorithms. However, recently published attack on the SIDH protocol [1] demonstrates that isogeny graphs require a more detailed study when they are used in real protocols. In this paper, we analyze the structure of isogeny graphs of degree l > 2 and consider a set of nodes of a special kind to which the attack [7] on path recovery in the graph is applicable.